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At least 19 records

Spacecraft Line-Of-Sight Jitter Mitigation and Management Lessons Learned and Engineering Best Practices

Predicting, managing, controlling, and testing spacecraft line-of-sight (LoS) jitter caused by micro-vibrations due to onboard internal disturbance sources is a formidable multidisciplinary engineering task. It is especially challenging for those missions hosting high-performance, vibration-sensitive optical sensor payloads with stringent pointing stability requirements. Both NASA and ESA are planning technically aggressive spaceflight missions that include ultra-high-performance optical payloads with delicate, highly vibration-sensitive scientific and observational instruments. The GN&C community of practice will need to leverage and build upon their collective experiences and lessons learned to better address future micro-vibration challenges. To identify lessons learned and best engineering practices the NASA Engineering & Safety Center (NESC) sponsored a two-day Spacecraft LoS Jitter Workshop in late 2019. The workshop’s goal was to provide a multidisciplinary forum to elicit deeper understanding of the issues related to solving the spacecraft LoS jitter/micro-vibration problem. A primary objective was to identify and share best practices, rules of thumb, and options for jitter-related activities. Representatives from NASA, JPL, ESA, along with NASA’s industrial partners, independent consultant subject matter experts, and members of academia participated in the workshop. This paper will describe the motivation for the NASA Spacecraft LoS Jitter Workshop and summarize the identified findings, observations, and recommendations.

Lessons Learned;↗

TPSAS-NF1676L-35881-DND

DEVELOP bridges the gap between NASA Earth Science and society, building capacity in both its participants and end-user organizations to better prepare them to handle the environmental challenges that face society.

Clayton, Amanda L↗

Technical Challenges in Reliable Microelectronics Packaging of Microelectromechanical Systems (MEMS) for Space Applications

MEMS have shown a significant promise in the last decade for a variety of applications such as air-bag, pressure sensors, accelerometer, microgyro, chemical sensors, artificial nose, etc. Standard semiconductor microelectronics packaging needs the integrated circuits (IC) to be protected from the harsh environment, and provide electrical communication with the other parts of the circuit, facilitate thermal dissipation efficiently, and impart mechanical strength to the silicon die. Microelectronics packaging involves wafer dicing, bonding, lead attachment, encapsulation to protect from the environment, electrical integrity, and package leak tests to assure the reliable IC packaging technology. Active elements or microstructures in MEMS devices often interfaces with the hostile environment where packaging leak tests and testing of such devices using chemical and mechanical parameters will be very difficult and expensive. Packaging of MEMS is significantly complex as they serve to protect from the environment and microstructures interact with the same environment to measure or affect the desired physical or chemical parameters. The most of the silicon circuitry is sensitive to temperature, moisture, magnetic field, light, and electromagnetic interference. The package must then protect the on-board silicon circuitry while simultaneously exposing the microsensor to the effect it measures to assure the packaging technology of MEMS. MEMS technology has a major application in developing a microspacecraft for space systems provided reliability of MEMS packaging technology is sufficiently addressed. This MEMS technology would eventually miniaturize many of the components of the spacecraft to reach the NASA's goal by building faster, cheaper, better, smaller spacecraft to explore the space more effectively. This paper discusses the latest developments in the MEMS technology and challenging technical issues in the packaging of hermetically sealed and non-hermetically sealed MEMS sensor devices for microspacecraft applications.

Ramesham, Rajeshuni↗

Making Metadata Better with CMR and MMT

Ensuring complete, consistent and high quality metadata is a challenge for metadata providers and curators. The CMR and MMT systems provide providers and curators options to build in metadata quality from the start and also assess and improve the quality of already existing metadata.

Quality↗

Building the RS-25 Engine for NASA’s Next Generation of Exploration.

NASA is aggressively pursuing a human lunar return to the Moon with the Artemis Program. The Space Launch System (SLS) is critical to the transportation architecture, providing both crew and cargo capability. To accelerate SLS development, NASA settled on space shuttle heritage propulsion technologies. Early missions will use repurposed RS-25 engines from the Shuttle Program adapted to SLS requirements. For future missions, however, NASA and engine contractor Aerojet Rocketdyne are restarting RS-25 production with a goal of using the latest manufacturing technologies to produce an RS-25 variant that will cost at least 30 percent less than the shuttle-era engines developed and flown for almost 30 years. The prospect of restarting the production line on these engines after many years and modifying the engine to reduce cost and better match the needs of the SLS vehicle presented unique challenges and opportunities for NASA and Aerojet Rocketdyne. NASA and AR are now deep into the process of adapting 16 RS-25 engines for the first four SLS Artemis flights and building the first RS-25 “Restart” engines for future Artemis missions. In addition to navigating programmatic, technical, and logistical challenges with the current RS-25 production work, NASA and AR have partnered to pursue new methods of building this engine through advanced manufacturing techniques to further reduce the cost and schedule required to build each RS-25 engine to contribute to the long-term affordability of the SLS vehicle. This presentation will discuss the goals for the restart program, the challenges, and results to date.

Jessica Jean Wood↗

Ames Collaborative Support Facility/Sustainability Base

This presentation is intended to motivate research initiatives at the Collaborative Support Facility on the Ames Research Center Campus. Awards and accomplishments will be highlighted, along with specific research objectives. Information technology challenges with also be introduced as a key initiative to be addressed to enable the deployment of novel technologies that will offer deeper insights into how better reduced energy consumption, improve occupant satisfaction and streamline building operations and maintenance activities.

algortihms↗

Assessment and Assurance of Microelectronics Packaging Technology of Microelectromechanical Systems (MEMS)

Microelectromechanical systems (MEMS) have shown a significant promise in the last decade for a variety of applications such as air-bag, pressure sensors, accelerometer, microgyro, etc. Standard semiconductor microelectronics packaging needs the integrated circuits to be protected from the harsh environment, and provide electrical communication with the other parts of the circuit, facilitate thermal dissipation efficiently, and impart mechanical strength to the silicon die. Microelectronics packaging involves wafer dicing, bonding, lead attachment, encapsulation to protect from the environment, electrical integrity, and package leak tests to assure the packaging technology. In the case of MEMS the microstructures (active elements) often interfaces with the hostile environment where packaging leak tests and testing of such devices using chemical and mechanical parameters will be very difficult and expensive. Packaging of MEMS is significantly complex as they serve to protect from the environment and microstructures interact with the same environment to measure or affect the desired physical or chemical parameters. The most of the silicon circuitry is sensitive to temperature, moisture, magnetic field, light, and electromagnetic interference. The package must then protect the on-board silicon circuitry while simultaneously exposing the microsensor to the effect it 'measures to assure the MEMS technology by lowering the risk to zero. MEMS technology has a major application in developing a microspacecraft for space systems provided assurance of MEMS technology is sufficiently addressed nondestructively. This technology would eventually miniaturize many of the components of the spacecraft to reach the NASA's safety and mission assurance goal by building faster, cheaper, better, smaller spacecraft to explore the space more effectively by teaming-up with the other NASA centers using the limited resources available. This paper discusses the latest developments in the MEMS technology and challenging issues in the packaging of hermetically sealed and non-hermetically sealed MEMS sensor devices based on silicon, poly-silicon, and other materials for microspacecraft applications considering the space environment and reliability assurance qualification guidelines in perspective. Acknowledgments: The above research work is supported by the NASA Electronics Parts and Packaging Program (NEPP) and performed by the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA under a contract with the NASA - Code Q for the Office of Safety and Mission Assurance Program 323-79.

Ramesham, Rajeshuni↗

NASA Phase2 Unlimited Rights Final Report Research and Technology for Aerospace Propulsion Systems (RTAPS) Task Order: ERA Advanced Core Compressor Technology Program

As part of the NASA Integrated Systems Research Program (ISRP), Environmentally Responsible Aviation (ERA) Project, NASA GRC and GE Aviation have partnered to investigate the technology barriers associated with improved fuel economy of large gas turbine engines. Crucial to improving fuel economy is the increase in pressure ratio (PR) of the core high pressure compressor (HPC). A key enabler to increasing HPC pressure ratios are new technology front stage airfoil designs that have higher efficiency, higher pressure ratios and improvements in front stage part-power operability. The purpose of this work is to design and test two high pressure ratio, high efficiency front block designs. The baseline design, hereafter referred to as Build 1, is similar to what would be found in a high efficiency 30:1 PR class HPC. A redesigned front block with improved blading will also be tested and hereafter be referred to as Build 2. The goal of Build 2 is to increase stage aero loading (increase stage pressure ratio) beyond Build 1 while maintaining equivalent efficiency and stall margin. The detailed inter-stage and traverse data from the two builds will be used to improve understanding of the complex flow physics at high-speed and part-speed conditions that impact performance and operability. By addressing, understanding and solving the challenges associated with aerodynamic losses and stage matching better design strategies can be incorporated in future core compressors with higher efficiency, thereby enabling improvement in mission fuel burn while still meeting operability requirements.

Axial Compressors↗

The International Space Station: Unique In-Space Testbed as Exploration Analog

Final assembly of the International Space Station (ISS) was completed in 2011. As articulated in the 2011 NASA Strategic Plan, the Agency's first goal is to extend and sustain human activities across the solar system. Thus, the emerging NASA vision is to launch a bold and ambitious new space initiative to enable human space exploration beyond low-Earth orbit to Lagrange points, the moon, near-Earth asteroids (NEAs), and Mars and its environs. To accomplish this vision, it is necessary to develop and validate innovative exploration technologies and operational concepts. With the extended life of the ISS to 2020 and possibly 2028, NASA has a mandate to maximize the potential of the Nation's newest National Laboratory. Exploration and ISS teams within NASA's Human Exploration and Operations Mission Directorate (HEOMD) have initiated a cooperative effort: the ISS Testbed for Analog Research (ISTAR), a high-fidelity operational analog that complements existing NASA terrestrial laboratory and field testing. To maximize use of the ISS platform to evaluate new exploration technologies, capabilities, and operational concepts to better comprehend and mitigate human spaceflight risks, ISTAR seeks out and encourages investigations dubbed "exploration detailed test objectives" (xDTOs). These xDTOs, building blocks of ISTAR missions, develop and optimize the operations concepts and the use of new technologies that should reduce risks and challenges facing astronauts on long exploration spaceflight voyages. In this paper, we describe (1) the rationale behind ISTAR, (2) a five-year strategic plan, (3) the approach for mission formulation, development, integration, and execution, (4) concepts for near-term missions that implement a phased approach for using ISS as an exploration testbed, and (5) the planned Mars mission simulation using the ISS. This paper will also document several challenges ISTAR must address to execute its missions.

Analog Mission↗

R2U2 in Space: System and Software Health Management for Small Satellites

In order for small but complex systems like rovers, SmallSats, or Unmanned Aircraft (UAS) to operate autonomously, they must have a real-time solution for assessing their own system health. System and Software Health Management (SHM) enables better detection of faulty sensors and software problems, and enables better fault management including mitigation of unpredicted fault scenarios in the absence of a human on-board. In recent work, we have developed a Responsive, Realizable, Unobtrusive Unit (R2U2) for on-board SHM of autonomous UAS and demonstrated its ability to detect faults during flight time. These faults, from sensor failures, to software problems, to malicious security attacks, can present as transient temporal faults that even humans are challenged to find. An R2U2 congfiuration is a modular combination of multiple types of temporal logic runtime observers with fault-specic Bayesian Nets and sensor filters. R2U2 reasons about both on-board hardware and software components; R2U2 itself can be instantiated as an independent FPGA (Field-Programmable Gate Array)-based conguration or as a software component running independently from other software on-board. Small satellites, such as CubeSats, also require on-board SHM and failure mitigation, as limited telemetry bandwidth does not allow the transmission of the entire system state for ground-based health management. However, the autonomous operation of satellites brings a set of challenges different from UAS, including the effects of radiation on non-rad-hard, low-cost components, and the harsher environment of space. We surmise that a new extension of R2U2 could be adapted to help better detect, for example, radiation errors in cheaper COTS (Commercial Off the Shelf) (not rad-hard) components often used in small space systems. Since small satellites often operate in coordination, we will also examine new ways of distributed monitoring of their communication and cooperation and real-time detection of off-nominal situations utilizing multiple satellites. This talk will discuss preliminary work and ideas for building on terrestrial success of system and software health management for the harsher, and differently challenging, environment of space.

Runtime Verification & Validation↗

Separation and Conditioning of Mars Atmospheric Gases via TSA

Space and planetary exploration almost always presents interesting and unusual engineering challenges. Separations engineering for chemical processes that are critical to humans working in space is no exception. The challenges are becoming clearer as we make the transition from concepts and planning to hardware development, and as we understand better the constraints and environments in which the processes must perform. The coming decade will see a robotic Mars exploration program that has recovered from recent setbacks and is building a knowledge and technology base for human exploration. One of the missions will carry a small chemical pilot plant for demonstrating the manufacture of rocket propellants and life support consumables from the low-pressure (0.01 atm) Martian atmosphere. By manufacturing and storing the fuel and consumables needed for human-return missions in situ, launch mass and landed mass are reduced by tons and missions become far less expensive. The front-end to the pilot plant is a solid-state atmosphere acquisition and separation unit based on temperature-swing adsorption (TSA). The unit produces purified and pressurized (to 1.0 atm) carbon dioxide to downstream reactors that will make methane and oxygen. The unit also produces a nitrogen-argon mixture as a valuable by-product for life support, inflatable structures, and propellant pressurization. With nighttime temperatures falling to -100 degrees C, power availability restricted to a few watts, and flawless operation critical to success, the dusty Martian surface is a difficult place to operate a remote plant. This talk will focus on how this TSA separation process is designed and implemented for this application, and how it might be used in the more distant future for human exploration.

Finn, John E.↗

Attenuation of Gas Turbulence by a Nearly Stationary Dispersion of Fine Particles

Turbulence attenuation by greater than a factor of two has been observed in many practical gas flows carrying volume fractions as small as 0.01% of dispersed particles. Particles which cause such attenuation usually are smaller than the smallest scales of the turbulence and have time constants 5 to 10 times greater than the time scale of a typical turbulent eddy. That is, strongly attenuating particles usually have Stokes numbers in the range of 5 to 10, indicating that they do not respond to the turbulent fluctuations, but instead just fall through the flow responding only to the mean flow. There are two mechanisms by which free falling particles may attenuate turbulence. First, the unresponsive particles act as a drag on the turbulent eddies, passing energy from the turbulent eddies to the small scale wakes of the particles where it is quickly dissipated by viscosity. The second mechanism is more complicated. Particles falling under gravity convert gravitational potential energy to turbulent velocity fluctuations. If the particles are large, this mechanism increases the overall turbulence level. However, with moderate size particles, the small scale turbulence generated apparently distorts the turbulent eddies leading to more rapid dissipation. Unfortunately, this conclusion is supported only by circumstantial evidence to date. The objectives of the experiment are to use microgravity to separate the two mechanisms. A region of nearly-isotropic decaying turbulence with zero mean flow will be formed in a box in the microgravity environment. Different sets of particles with Stokes numbers in the range of 2 to 20 will be dispersed in the flow. With zero gravity and no mean fluid velocity the particles will have zero mean velocity. With the large Stokes numbers, the fluctuating velocities will also be small. Therefore, the only attenuation mechanism will be the direct action of the particles on the turbulence. Control experiments will also be done in which the particles fall through the measurement volume. Measurements will be acquired using a high resolution image velocimetry (PIV) system being developed specifically for work in particle-laden flows. The measurements will include the decay of the turbulence kinetic energy under various particle loadings. The spatial spectra of the turbulence will also be measured. In a second set of experiments, the interaction of a single eddy with a collection of nearly stationary particles will be examined. The eddy will be a vortex ring emitted by a jet pulse through an orifice. The distortion of the vortex under the influence of the particles will be examined to gain a better understanding of how fine particles can cause such large reductions in turbulence levels. This experiment could not be conducted in terrestrial gravity because the high particle velocities would overwhelm the relatively low speed motion of the vortex ring. This experimental program is just getting underway. The initial challenge is to build a closed facility containing reasonably homogeneous and isotropic turbulence with zero mean velocity. Our approach is to use a set of synthetic jets mounted on the periphery of a transparent plexiglass box to create the turbulence. A synthetic jet is a plenum chamber with an orifice open to the volume of interest. The volume of the chamber fluctuates periodically so alternately a jet is ejected from the volume or flow is drawn back in as a sink. The asymmetry of this situation results in a net transport of momentum and kinetic energy into the volume of interest. The present apparatus includes eight synthetic jets each powered independently by a six inch loudspeaker. The synthetic jets discharge through ejector tubes to increase the scale of the turbulence. Construction of the apparatus is now complete and preliminary flow visualization studies have been conducted. The PIV system is also under development. A compact dual-pulse YAG laser has been acquired as the light source and special software is under development to allow simultaneous measurements of both the particle phase and the fluid phase (marked by fine tracers).

Paris, A. D.↗

Mission Advantages of Constant Power, Variable Isp Electrostatic Thrusters

Electric propulsion has moved from station-keeping capability for spacecraft to primary propulsion with the advent of both the Deep Space One asteroid flyby and geosynchronous spacecraft orbit insertion. In both cases notably more payload was delivered than would have been possible with chemical propulsion. To provide even greater improvements electrostatic thruster performance could be varied in specific impulse, but kept at constant power to provide better payload or trip time performance for different mission phases. Such variable specific impulse mission applications include geosynchronous and low earth orbit spacecraft stationkeeping and orbit insertion, geosynchronous reusable tug missions, and interplanetary probes. The application of variable specific impulse devices is shown to add from 5 to 15% payload for these missions. The challenges to building such devices include variable voltage power supplies and extending fuel throughput capabilities across the specific impulse range.

Oleson, Steven R.↗

Operational Assessment of Apollo Lunar Surface Extravehicular Activity

Quantifying the operational variability of extravehicular activity (EVA) execution is critical to help design and build future support systems to enable astronauts to monitor and manage operations in deep-space, where ground support operators will no longer be able to react instantly and manage execution deviations due to the significant communication latency. This study quantifies the operational variability exhibited during Apollo 14-17 lunar surface EVA operations to better understand the challenges and natural tendencies of timeline execution and life support system performance involved in surface operations. Each EVA (11 in total) is individually summarized as well as aggregated to provide descriptive trends exhibited throughout the Apollo missions. This work extends previous EVA task analyses by calculating deviations between planned and as-performed timelines as well as examining metabolic rate and consumables usage throughout the execution of each EVA. The intent of this work is to convey the natural variability of EVA operations and to provide operational context for coping with the variability inherent to EVA execution as a means to support future concepts of operations.

planning and scheduling↗

In-Space Transportation for NASA's Evolvable Mars Campaign

As the nation embarks on a new and bold journey to Mars, significant work is being done to determine what that mission and those architectural elements will look like. The Evolvable Mars Campaign, or EMC, is being evaluated as a potential approach to getting humans to Mars. Built on the premise of leveraging current technology investments and maximizing element commonality to reduce cost and development schedule, the EMC transportation architecture is focused on developing the elements required to move crew and equipment to Mars as efficiently and effectively as possible both from a performance and a programmatic standpoint. Over the last 18 months the team has been evaluating potential options for those transportation elements. One of the key aspects of the EMC is leveraging investments being made today in missions like the Asteroid Redirect Mission (ARM) mission using derived versions of the Solar Electric Propulsion (SEP) propulsion systems and coupling them with other chemical propulsion elements that maximize commonality across the architecture between both transportation and Mars operations elements. This paper outlines the broad trade space being evaluated including the different technologies being assessed for transportation elements and how those elements are assembled into an architecture. Impacts to potential operational scenarios at Mars are also investigated. Trades are being made on the size and power level of the SEP vehicle for delivering cargo as well as the size of the chemical propulsion systems and various mission aspects including Inspace assembly and sequencing. Maximizing payload delivery to Mars with the SEP vehicle will better support the operational scenarios at Mars by enabling the delivery of landers and habitation elements that are appropriately sized for the mission. The purpose of this investigation is not to find the solution but rather a suite of solutions with potential application to the challenge of sending cargo and crew to Mars. The goal is that, by building an architecture intelligently with all aspects considered, the sustainable Mars program wisely invests limited resources enabling a long-term human Mars exploration program.

Percy, Thomas K.↗

Fundamental Investigation of Silicon Anode in Lithium-Ion Cells

Silicon is a promising and attractive anode material to replace graphite for high capacity lithium ion cells since its theoretical capacity is ~10 times of graphite and it is an abundant element on Earth. However, there are challenges associated with using silicon as Li-ion anode due to the significant first cycle irreversible capacity loss and subsequent rapid capacity fade during cycling. Understanding solid electrolyte interphase (SEI) formation along with the lithium ion insertion/de-insertion kinetics in silicon anodes will provide greater insight into overcoming these issues, thereby lead to better cycle performance. In this paper, cyclic voltammetry and electrochemical impedance spectroscopy are used to build a fundamental understanding of silicon anodes. The results show that it is difficult to form the SEI film on the surface of a Si anode during the first cycle; the lithium ion insertion and de-insertion kinetics for Si are sluggish, and the cell internal resistance changes with the state of lithiation after electrochemical cycling. These results are compared with those for extensively studied graphite anodes. The understanding gained from this study will help to design better Si anodes, and the combination of cyclic voltammetry with impedance spectroscopy provides a useful tool to evaluate the effectiveness of the design modifications on the Si anode performance.

Wu, James J.↗

Strain Monitoring of Flexible Structures

One of the biggest challenges facing NASA's deep space exploration goals is structural mass. A long duration transit vehicle on a journey to Mars, for example, requires a large internal volume for cargo, supplies and crew support. As with all space structures, a large pressure vessel is not enough. The vehicle also requires thermal, micro-meteoroid, and radiation protection, a navigation and control system, a propulsion system, and a power system, etc. As vehicles get larger, their associated systems also get larger and more complex. These vehicles require larger lift capacities and force the mission to become extremely costly. In order to build large volume habitable vehicles, with only minimal increases in launch volume and mass, NASA is developing lightweight structures. Lightweight structures are made from non-metallic materials including graphite composites and high strength fabrics and could provide similar or better structural capability than metals, but with significant launch volume and mass savings. Fabric structures specifically, have been worked by NASA off and on since its inception, but most notably in the 1990's with the TransHAB program. These TransHAB developed structures use a layered material approach to form a pressure vessel with integrated thermal and micro-meteoroid and orbital debris (MMOD) protection. The flexible fabrics allow the vessel to be packed in a small volume during launch and expand into a much larger volume once in orbit. NASA and Bigelow Aerospace recently installed the first human-rated inflatable module on the International Space Station (ISS), known as the Bigelow Expandable Activity Module (BEAM) in May of 2016. The module provides a similar internal volume to that of an Orbital ATK Cygnus cargo vehicle, but with a 77% launch volume savings. As lightweight structures are developed, testing methods are vital to understanding their behavior and validating analytical models. Common techniques can be applied to fabric materials, such as tensile testing, fatigue testing, and shear testing, but common measurement techniques cannot be used on fabric. Measuring strain in a material and during a test is a critical parameter for an engineer to monitor the structure during the test and correlate to an analytical model. The ability to measure strain in fabric structures is a challenge for NASA. Foil strain gauges, for example, are commonplace on metallic structures testing, but are extremely difficult to interface with a fabric substrate. New strain measuring techniques need to be developed for use with fabric structures. This paper investigates options for measuring strain in fabric structures for both ground testing and in-space structural health monitoring. It evaluates current commercially available options and outlines development work underway to build custom measurement solutions for NASA's fabric structures.

Litteken, Douglas A.↗

Sweat Rates During Continuous and Interval Aerobic Exercise: Implications for NASA Multipurpose Crew Vehicle (MPCV) Missions

Aerobic deconditioning is one of the effects spaceflight. Impaired crewmember performance due to loss of aerobic conditioning is one of the risks identified for mitigation by the NASA Human Research Program. Missions longer than 8 days will involve exercise countermeasures including those aimed at preventing the loss of aerobic capacity. The NASA Multipurpose Crew Vehicle (MPCV) will be NASA's centerpiece architecture for human space exploration beyond low Earth orbit. Aerobic exercise within the small habitable volume of the MPCV is expected to challenge the ability of the environmental control systems, especially in terms of moisture control. Exercising humans contribute moisture to the environment by increased respiratory rate (exhaling air at 100% humidity) and sweat. Current acceptable values are based on theoretical models that rely on an "average" crew member working continuously at 75% of their aerobic capacity (Human Systems Integration Requirements Document). Evidence suggests that high intensity interval exercise for much shorter durations are equally effective or better in building and maintaining aerobic capacity. This investigation will examine sweat and respiratory rates for operationally relevant continuous and interval aerobic exercise protocols using a variety of different individuals. The results will directly inform what types of aerobic exercise countermeasures will be feasible to prescribe for crewmembers aboard the MPCV.

Ryder, Jeffrey W.↗